自相关对MEWMA控制图影响的模拟研究

Simulation Study on the Influence of Autocorrelation Structure on MEWMA Control Chart

为了分析样本协方差不同时自相关结构对常规多元控制图监测偏移能力的影响,针对传统样本协方差矩阵S1和基于相邻向量差数据构建的协方差矩阵S2的两种不同取值,通过Monte Carlo模拟对比忽略自相关的原始数据和考虑自相关时基于多变量时间序列模型VAR(1)构建的残差数据的两种情况,以平均运行链长比较了不同均值偏移大小及不同自相关结构下多元控制图的性能。对比结果发现:基于VAR(1)模型的残差MEWMA控制图整体表现更佳,可以更快地捕捉到均值的变化,且该控制图在均值偏移大于一个标准偏差时监测效果更明显;当S2作为总体协方差估计值时,基于残差数据构建的MEWMA控制图受控平均运行链长ARL0较低,但该方法能更快地检测到均值的偏移。最后通过一个案例验证了结论的准确性。

To analyze the effect of autocorrelation structure on the monitoring of conventional multivariate control charts when the sample covariance is different,the two different estimates of traditional sample covariance matrix S1 and covariance matrix S2 constructed based on adjacent vector difference data matrix,the Monte Carlo simulation is used to compare the original data of the autocorrelation and the residual data constructed based on the multivariate time series model VAR(1)when considering autocorrelation.The performance of multivariate control graphs with different mean shift sizes and different autocorrelation structures,which is compared by ARL.The comparison results show that the residual MEWMA control chart based on VAR(1)model performs better,it can capture changes in the mean faster,and the control chart has a more obvious monitoring effect when the mean shift is greater than one standard deviation.When S2 is used as the overall covariance estimate,the ARL0 of control chart is lower,which is constructed,based on the residual data.However,it can detect the deviation of the mean faster.Finally,the accuracy of the conclusion is verified by a case.